A stationary source is emitted sound at a fixed frequency f 0 , which is reflected by two cars approaching the source. The difference between the is frequencies of sound reflected from the car is 1 . 2 % of f 0 . What is the difference in the speed of the cars (in m s - 1 )? The cars are moving at constant speeds much smaller than the speed of sound which is 330 m s - 1

Question

A stationary source is emitted sound at a fixed frequency f 0 , which is reflected by two cars approaching the source. The difference between the is frequencies of sound reflected from the car is 1 . 2 % of f 0 . What is the difference in the speed of the cars (in m s - 1 )? The cars are moving at constant speeds much smaller than the speed of sound which is 330 m s - 1,

MARKS App · Accepted Answer

Firstly, car will be treated as an observer which is approaching the source. Then, it will be treated as a source, which is moving in the direction of sound. Hence, f 1 = f o v + v 1 v - v 1 f 2 = f o v + v 2 v - v 2 ∴ f 1 - f 2 = 1.2 100 f o = f o v + v v + v 1 - v + v 2 v - v 2 Or 1.2 100 f o = 2 v v 1 - v 2 v - v 1 v - v 2 f o a s v 1 a n d v 2 are very very less than v. We can write, v - v 1 o r v - v 2 ≈ v . ∴ 1.2 100 f o = 2 v 1 - v 2 v f o O r v 1 - v 2 = v × 1.2 200 = 300 × 1 .2 200 = 1 .98 m s - 1

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